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Resonance and Hybrid Structures02:16

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According to the theory of resonance, if two or more Lewis structures with the same arrangement of atoms can be written for a molecule, ion, or radical, the actual distribution of electrons is an average of that shown by the various Lewis structures.
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Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...
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Double resonance techniques in Nuclear Magnetic Resonance (NMR) spectroscopy involve the simultaneous application of two different frequencies or radiofrequency pulses to manipulate and observe two distinct nuclear spins. One important application of double resonance is spin decoupling, which selectively suppresses coupling with one type of nucleus while observing the NMR signal from another nucleus, simplifying the spectrum and enhancing resolution.
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Spin systems where the difference in chemical shifts of the coupled nuclei is greater than ten times J are called first-order spin systems. These nuclei are weakly coupled, and their chemical shifts and coupling constant can generally be estimated from the well-separated signals in the spectrum.
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Atomic and Molecular Complex Resonances from Real Eigenvalues Using Standard (Hermitian) Electronic Structure

Arie Landau, Idan Haritan, Petra Ruth Kaprálová-Žd'ánská1,2

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This study presents a novel method to calculate complex resonance eigenvalues using standard electronic structure packages. The approach utilizes analytical continuation, enabling accurate computation of resonance positions and widths for various systems.

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Area of Science:

  • Quantum Chemistry
  • Atomic and Molecular Physics
  • Computational Chemistry

Background:

  • Complex eigenvalues, or resonances, are crucial in physics and chemistry, particularly in phenomena like autoionization and predissociation.
  • Calculating these resonances typically requires specialized electronic structure codes and methods, which can be computationally intensive and complex.

Purpose of the Study:

  • To demonstrate a method for calculating complex resonance eigenvalues (positions and widths) using widely available, standard electronic structure packages.
  • To provide an alternative to complex, non-standard computational approaches for resonance calculations.

Main Methods:

  • Utilizing analytical continuation procedures, specifically Padé approximants, to access the complex energy plane.
  • Leveraging the properties of finite basis sets to create analytical passages from the real to the complex energy axis.

Main Results:

  • Successfully calculated autoionization Feshbach resonances for helium, hydrogen anion, and hydrogen molecule.
  • Achieved excellent agreement between calculated resonance eigenvalues and existing theoretical and experimental results.

Conclusions:

  • The proposed method offers a practical and efficient way to compute complex resonance eigenvalues with standard computational tools.
  • This approach simplifies the study of resonances in various physical and chemical systems, enhancing accessibility for researchers.